Stars clusters undergo core collapse on a thermal time scale. This results follows from a detailed simulations in the form of N-body, Fokker-Planck, and gas sphere models. The shrinking of the core, both in size as well as mass, is often heuristically attributed to the negative heat capacity of gravity, as follows from the virial theorem. However, this argument only describes the overall contraction of the inner parts of a star cluster and does not address the evolution of the core mass. A linear stability analysis of the isothermal sphere is presented for different choices of heat conductivity.